Dominick and Elliot pose looking at the camera, in a photograph taken by Robert Mapplethorpe in 1979. One of them is crucifying the other upside-down. Elliot – or is it Dominick? – is suspended by his ankles, with his arms pulled outward and chained in the position of a crucified body, in a picture that ambitiously and convincingly quotes a 17th-century painting by Caravaggio of the martyrdom of St Peter. Just as Caravaggio showed the strain of the men doing the tough work of turning the cross upside-down with a man nailed to it, Mapplethorpe captures the insouciant way this man's torturer, bare-chested and looking at us from a massive bearded head, holds a cigarette in front of his crotch. It's the little human details that make a scene real.

This is consensual torture, one of Mapplethorpe's spectacularly intimate pictures of the sadomasochist lifestyle he enjoyed. Another, of a man in a mask in a basement where he might be a prisoner, is called Jim, Sausalito.

Now Jim, Dominick and Elliot are about to go on view in Eastbourne, of all places, in a luxuriant survey of Mapplethorpian decadence at the sedate, south-coast town's Towner gallery. The striking Le Corbusier-like architecture of the Towner that opened last year tells visitors pretty clearly to expect confrontational modern art, so local Disgusteds probably won't even reach the exhibition floor. Still, to judge from the number of shops in Eastbourne that specialise in medical aids for the elderly, it might be an idea to keep a CPR specialist on hand.

My heart was pounding after some time alone with Mapplethorpe's pictures. The exhibition begins with portraits of himself and Patti Smith. In her composition Land, the rock poet, who lived with Mapplethorpe at the Chelsea Hotel when they were in their 20s, creates a mythology that mirrors his leather fantasies. "The boy looked at Johnny," she sings, and then a rockabilly nightmare of switchblades and erotic pain unfolds in a glassy stilled imagery of sex and death: Johnny goes down on his knees and all he can see are "horses, horses, horses…"

The iconography of this song is reproduced in a 1983 self-portrait in which Mapplethorpe poses in a leather jacket wielding a switchblade with his hair slicked into an ornate meta-rocker quiff. Another self-portrait shows his head from behind, greased and shaped to form, with the jacket, an abstract design like a sexually charged Rodchenko poster – or a fantasy album cover. Here is art as dark romance, as rock'n'roll.

Mapplethorpe was to shoot to fame (the suggestiveness of that expression would not have escaped him: his 1985 photograph Gun Blast shows what looks like sperm firing from a pistol) soon after his death in 1989. Already an art world cult, it was the controversy over a posthumous exhibition of his works at the Corcoran Gallery, close to the White House in Washington DC, that turned him into a household name in America. All the polarities of American life that controversy unleashed are still in place as Christian zealots ride the Tea Party bus. But where other artists may stumble into controversy or respond to it with protestations of innocence, Mapplethorpe was in many ways as Christian as his accusers – in the sense that he apparently believed in the devil. No, let's put it more clearly: he believed he was the devil. In a self-portrait from 1983, he poses in front of a pentagram with a machine-gun: Satan's terrorist. In a staggering work from 1988, he magnifies his own eyes to the scale of Michelangelo's David. Those glassy peepers stare at you fiercely, and it is hard to resist associations with The Exorcist. In his most famous self-image, as he sits, ill and emaciated, holding a cane with a carved skull, he is doing more than acknowledge mortality: he is claiming to be the new King Death, inheriting the title Andy Warhol whose fragile head he portrayed with a transcendental clarity, in a portrait so real you feel you could reach into it and hold it, stroke the silver wig.

Mapplethorpe's technical brilliance as a photographer is such as to transform each of his images from a document to a flash of rapture. The whites are often so bright, in their cloak of night, as to go past your eyes straight into your brain, or your body. White light, white heat. The result is to give forms three-dimensional reality. When you look at a Mapplethorpe nude, it hits you, consciously or subconsciously, that it does not work with the safety and control of a glossy photo of flesh. Instead, it feels as if you are close to a living body. Mapplethorpe was fascinated by sculpture, and this exhibition includes some of his own, wall objects depicting stars and crosses, whose greatest interest is to draw your attention to the sculpted quality of the photographs themselves.

Last year the Accademia Gallery in Florence made the same point by showing his works next to Michelangelo's David: it was an effective double act. Mapplethorpe quotes Michelangelo as seriously as he quotes Caravaggio. His picture in Eastbourne of Lisa Lyon seen from behind, her torso bound and spinal column deeply etched, is a homage to the Renaissance sculptor and his obsession with backs.

Formal beauty, art-historical echoes – but you could do Mapplethorpe a disservice by trying to make him respectable. This exhibition only makes one slip when it claims his flower photographs are his most "erotic" works. Maybe, but the picture of a cock bound in leather next to a bronze figurine of the devil is probably lewder. The brilliance of this selection, from the Artist Rooms collection donated by Anthony d'Offay in 2008, is that it gets us close to the real man, the real artist. It has a rawness and also a humour that often eludes selections made by overly academic curators.

Not many photographers have so ruthlessly expressed a personal vision through the camera.

Mapplethorpe found the style that could match his intensely romantic nature, and deployed it with great courage. Like his father-figure Warhol, he vaunted an obsession with death. But among the leathers and the skulls, what makes him a great, enduring artist is his appetite for life. A passion for existence shines out of those crystal eyes.

•Robert Mapplethorpe is showing at Towner, Eastbourne from 25 September to 21 November. Details: nationalgalleries.org/artistrooms